Parameterised post-Newtonian formalism for the effective field theory of dark energy via screened reconstructed Horndeski theories

TL;DR

This paper connects the parameterised post-Newtonian formalism with the effective field theory of dark energy within Horndeski theories, enabling comprehensive tests of gravity across scales by reconstructing models with screening mechanisms.

Contribution

It introduces a method to reconstruct Horndeski theories from EFT functions and derive PPN parameters, linking large-scale cosmological and astrophysical tests of gravity.

Findings

Derived PPN parameters for reconstructed models with screening mechanisms.

Established conditions for models to have significant cosmological modifications while satisfying astrophysical bounds.

Performed post-Newtonian expansion to connect theory with observational tests.

Abstract

We bring together two popular formalisms which generically parameterise deviations from General Relativity on astrophysical and cosmological scales, namely the parameterised post-Newtonian (PPN) formalism and the effective field theory (EFT) of dark energy and modified gravity. These separate formalisms are successfully applied to independently perform tests of gravity in their respective regimes of applicability on vastly different length scales. Nonlinear screening mechanisms indeed make it imperative to probe General Relativity across a wide range of scales. For a comprehensive interpretation of the complementary measurements it is important to connect them to effectively constrain the vast gravitational model space. We establish such a connection within the framework of Horndeski scalar-tensor theories restricted to a luminal propagation speed of gravitational waves. This is possible via the reconstruction of the family of linearly degenerate covariant Horndeski actions from the set of EFT functions and the subsequent derivation of the PPN parameters from the reconstructed theory. We outline the required conditions which ensure a reconstructed Horndeski model possesses a screening mechanism that enables significant modifications on cosmological scales while respecting stringent astrophysical bounds. Employing a scaling method, we then perform the general post-Newtonian expansion of the reconstructed models to derive their PPN parameters $\gamma$ and $\beta$ in their screened regimes.